A blistering anti-Obama documentary — “2016: Obama’s America” — has exploded on movie screens just as the president prepares for his big moment before the Democratic National Convention next week.

The film debuted on one screen in Houston last month, but is now in 1,091 theaters — including six in New York City — and is expected to be in 1,700 this weekend.

In the film, author Dinesh D’Souza traces Obama’s roots from Kenya, through Indonesia and Hawaii to document how he is ideologically rooted in the Third World.

D’Souza, a former Ronald Reagan policy adviser, points out that when Obama was a teen, his mentor was Frank Marshall Davis, a communist.

The movie also emphasizes the leftist, anti-colonialist views of Obama’s father, and points to an article written by the senior Obama that called for stricter regulation of business and unbridled taxation.

The movie, based on D’Souza’s 2011 book, “The Roots of Obama’s Rage,” has grossed $11.6 million, making it the most popular conservative documentary of all time. It ranked eighth in last weekend’s box office.

Even D’Souza is surprised by the film’s success.

“Our film is not a ‘Don’t vote for Obama film,’” he told The Post. “It’s a get-to-know-Obama film. The goal of the film is to shape the national debate.”

“The birthers are unhappy with me because I don’t go down the birther road,” said D’Souza, who has a new sequel book out “Obama’s America: Unmasking the American Dream.”

“The liberals have been trying to ignore it, and we are getting a little too big to ignore.”

The film is being compared to Academy-Award winning filmmaker Michael Moore’s 2004 anti-Bush movie “Fahrenheit 9/11.” The Obama flick isn’t expected to gross the $119 million Moore saw but has already exceeded its $10 million production and promotion costs.

Much of the promotion of the film has cost little, because it was discussed mostly on conservative talk shows around the country.

But what impact will it have on the presidential race?

“A film that attracts people’s attention can have a big impact on the election,” said Ron Faucheux, former editor of Campaigns and Elections magazine.

“But if the only people who see it are people against Obama, it won’t have much of an impact. The big question is whether people believe it.”

D’Souza had fan support in the six New York movie theaters showing it yesterday.

“We want to hand out flyers for people to come see it,” Ruth Hoffman, 67, an Upper East Side Republican, said.

“We learned about the president’s past . . . His whole background is riddled with people who are anti-American and consider America to be a bad place,” she said after watching it at the Regal Union Square.

Jordan Regenz, a 24-year-old independent voter from Great Neck, LI, said the movie swayed him.

“Going in, I didn’t know if it was for or against him, and obviously it turns out to be against him,” Regenz said.

“It sounds like the filmmaker is trying to get you to think that Obama doesn’t want what’s best for America. The film brings up points, and if they were true, then I would be swayed to not vote for Obama.”

Carl Litwak, 69, a retired Gramercy Park independent, said the movie scared him when it comes to Obama policies.

“I thought it was terrific,” Litwak said. “The theater was more than half full. People were applauding when it was over.”